Did your employer withhold NY state tax? Did you physically work in NYS at anytime during the year?
If the answer to both questions is no, you do not need to file a NY return.
No matter where you worked, New York generally considers the income from working remotely for a New York employer to be New York income.
If you work outside the state as a job requirement, you are only subject to New York State income tax on the days you work in New York. But if you work outside New York for your own convenience, you are subject to New York State income tax on all your income. Pennsylvania, Nebraska, Delaware and Arkansas have the same rule.
Also, see these more recent discussions, wherein posters say it requires at least 1 day in NY to be subject to NYS income tax, even when it's for your own convenience. https://ttlc.intuit.com/community/state-taxes/discussion/re-starting-new-job-with-office-in-new-york...
and
https://ttlc.intuit.com/community/taxes/discussion/re-will-i-owe-any-california-income-tax/01/276936...
